Step |
Hyp |
Ref |
Expression |
1 |
|
cnmpt21.j |
|
2 |
|
cnmpt21.k |
|
3 |
|
cnmpt21.a |
|
4 |
|
cnmpt21.l |
|
5 |
|
cnmpt21.b |
|
6 |
|
cnmpt21.c |
|
7 |
|
df-ov |
|
8 |
|
simprl |
|
9 |
|
simprr |
|
10 |
|
txtopon |
|
11 |
1 2 10
|
syl2anc |
|
12 |
|
cnf2 |
|
13 |
11 4 3 12
|
syl3anc |
|
14 |
|
eqid |
|
15 |
14
|
fmpo |
|
16 |
13 15
|
sylibr |
|
17 |
|
rsp2 |
|
18 |
16 17
|
syl |
|
19 |
18
|
imp |
|
20 |
14
|
ovmpt4g |
|
21 |
8 9 19 20
|
syl3anc |
|
22 |
7 21
|
syl5eqr |
|
23 |
22
|
fveq2d |
|
24 |
|
eqid |
|
25 |
6
|
eleq1d |
|
26 |
|
cntop2 |
|
27 |
5 26
|
syl |
|
28 |
|
toptopon2 |
|
29 |
27 28
|
sylib |
|
30 |
|
cnf2 |
|
31 |
4 29 5 30
|
syl3anc |
|
32 |
24
|
fmpt |
|
33 |
31 32
|
sylibr |
|
34 |
33
|
adantr |
|
35 |
25 34 19
|
rspcdva |
|
36 |
24 6 19 35
|
fvmptd3 |
|
37 |
23 36
|
eqtrd |
|
38 |
|
opelxpi |
|
39 |
|
fvco3 |
|
40 |
13 38 39
|
syl2an |
|
41 |
|
df-ov |
|
42 |
|
eqid |
|
43 |
42
|
ovmpt4g |
|
44 |
8 9 35 43
|
syl3anc |
|
45 |
41 44
|
syl5eqr |
|
46 |
37 40 45
|
3eqtr4d |
|
47 |
46
|
ralrimivva |
|
48 |
|
nfv |
|
49 |
|
nfcv |
|
50 |
|
nfcv |
|
51 |
|
nfmpo1 |
|
52 |
50 51
|
nfco |
|
53 |
|
nfcv |
|
54 |
52 53
|
nffv |
|
55 |
|
nfmpo1 |
|
56 |
55 53
|
nffv |
|
57 |
54 56
|
nfeq |
|
58 |
49 57
|
nfralw |
|
59 |
|
nfv |
|
60 |
|
nfcv |
|
61 |
|
nfmpo2 |
|
62 |
60 61
|
nfco |
|
63 |
|
nfcv |
|
64 |
62 63
|
nffv |
|
65 |
|
nfmpo2 |
|
66 |
65 63
|
nffv |
|
67 |
64 66
|
nfeq |
|
68 |
|
opeq2 |
|
69 |
68
|
fveq2d |
|
70 |
68
|
fveq2d |
|
71 |
69 70
|
eqeq12d |
|
72 |
59 67 71
|
cbvralw |
|
73 |
|
opeq1 |
|
74 |
73
|
fveq2d |
|
75 |
73
|
fveq2d |
|
76 |
74 75
|
eqeq12d |
|
77 |
76
|
ralbidv |
|
78 |
72 77
|
syl5bb |
|
79 |
48 58 78
|
cbvralw |
|
80 |
47 79
|
sylib |
|
81 |
|
fveq2 |
|
82 |
|
fveq2 |
|
83 |
81 82
|
eqeq12d |
|
84 |
83
|
ralxp |
|
85 |
80 84
|
sylibr |
|
86 |
|
fco |
|
87 |
31 13 86
|
syl2anc |
|
88 |
87
|
ffnd |
|
89 |
35
|
ralrimivva |
|
90 |
42
|
fmpo |
|
91 |
89 90
|
sylib |
|
92 |
91
|
ffnd |
|
93 |
|
eqfnfv |
|
94 |
88 92 93
|
syl2anc |
|
95 |
85 94
|
mpbird |
|
96 |
|
cnco |
|
97 |
3 5 96
|
syl2anc |
|
98 |
95 97
|
eqeltrrd |
|